Calculation of stress intensity factors based on mode I crack opening integral parameters

Abstract

We present stress intensity factor assessment using nodal displacements of the crack surfaces determined by the finite element method for cracked bodies. The equation is solved by expanding the crack opening displacement in the Chebyshev function, where crack front asymptotic behavior corresponds to the regulations of the linear elastic fracture mechanics. Results of the stress intensity factor calculations are obtained for test problems with analytical solution. Crack opening displacements are defined with the help of the 3D SPACE software package designed to model mixed variational formulation of the finite element method for displacements and strains of the thermoelastic boundary value problems.There are different approaches to the calculations of the stress intensity factor K I involving the results of the stress-strain analysis for the cracked bodies by means of the finite element method (FEM). Depending on the model design peculiar characteristics of the modern technical tools (inhomogeneity, complex geometry, mixed boundary conditions, etc.) the stress-strain state data in the form of discontinuous fields for the finite element method for displacements, strains and stresses is required for FEM implementation. There are no universal recommendations for using this data within the framework of technology and operational direction of the FEM for K I calculation.Results of the expert investigations of the theoretical fracture mechanics parameters implemented in the ABAQUS software [1] and its practical application has shown that these recommendations are unlikely to be developed in the nearest future. Differences related to calculations occur in case of a three-dimensional geometrical model which depicts adequately tendency to the quasiregular discretization of the field by the finite elements with the exception of the choice of the calculation method for K I .The J-integral and weight function methods are widely applied in engineering. The weight function method includes data on surface stresses at the crack edges to obtain approximate formulas to simplify the calculations for the different specimens at laboratory testing and stress-strain state analysis for the modern technical structural components [2]. However, errors in the nodal displacement calculations are more critical when the stress is defined by means of the finite element method while using the superposition method. An alternative approach based on the nodal displacements for K I calculations and implemented in commercial software as well as in the specialized software for FEM becomes topical for different fields of the fracture mechanics [3]. Nodal displacements should be taken into account according to their nature because the error in the approximate solution of the FEM displacement analysis is minimal and there is no need in the additional conversions (average, approximation of derivatives, distance from crack front and so on).We introduce the integral parameters for displacements along the line on the crack surface implemented in the 3D SPACE...

Determination of displacements on the surface of 3D flat cracks in an unbounded elastic medium

“…Studies of the accuracy of calculation of SIFs from displacements in the modeling of fatigue crack growth [3] show the application of this approach to be cost-effective on finite element calculations. Studies of the second-kind Chebyshev polynomial expansion of normal displacements along the normal to crack front on the basis of FEM data [4] corroborate the conclusions made in [3].…”

“…The reliability of the method has been confirmed by comparing the calculated results with analytical solutions and data obtained by other methods. 4. The efficiency of the method as an alternative way of the MSIE implementation consists in a considerable reduction, for practical calculations, of the matrix dimension of resolving systems of algebraic equation, efforts and time for their formation and the finite element discretization of the surface.…”